Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 7x + 3$ and $ BC = 2x + 43$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {7x + 3} = {2x + 43}$ Solve for $x$ $ 5x = 40$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 7({8}) + 3$ $ BC = 2({8}) + 43$ $ AB = 56 + 3$ $ BC = 16 + 43$ $ AB = 59$ $ BC = 59$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {59} + {59}$ $ AC = 118$